Europe is in a "race against time" to save its system of passport-free travel and must move fast to tighten control of migration over its external borders, European Council President Donald Tusk said on Thursday.

Citing Sweden's move to reimpose checks on arrivals from other EU countries and new measures in Germany and Slovenia, he told a news conference at a summit on migration on Malta that these showed EU states were under "huge pressure."

"Saving Schengen is a race against time," the former Polish premier said of the open border system among European states.

"And we are determined to win that race." That would require implementing the series of measures agreed amid great dispute among EU governments over the past few months, he said. "This includes, first and foremost, restoring external border control. Without effective border control, the Schengen rules will not survive."

"We must hurry, but without panic," he said after a summit with African leaders that will be followed by an emergency EU summit later on Thursday in Valletta to discuss migration and notably efforts to secure a deal with Turkey to slow departures.